In particular, the state police chief in New Mexico is making headlines after he promised to buy a plane ticket for Charlie Hill, a man suspected of murdering a New Mexico state police officer in 1971.

“Hill is one of a number of America’s most-wanted fugitives who made new lives for themselves in Cuba after fleeing the U.S. years ago and are now the focus of possible extradition under restored relations,” said an article from the Associated Press on ABC New‘s website

Hill is accused of killing the officer, then escaping with two other accomplices by hijacking a plane at the Albuquerque airport and commandeering it to Cuba. The two other men involved in the crime eventually died in Cuba.

The high profile case is one that has not escaped politicians’ attention. Sen. Tom Udall, who recently went on a congressional delegation to Cuba, said Hill should be extradited.

Despite poor relations in the past, Cuba has been surprisingly helpful with returning fugitives to the U.S.

“In September 2011, Cuba handed over to U.S. authorities Denis Catania, 49, and Diana Camacho, 26, both formerly of Voorhees, to face kidnapping, murder, and arson charges in the death of Somerdale resident Ross Heimlich, 23, whose charred body was found in a torched car in Hammonton in 2010. The pair fled to Florida, then to various Caribbean nations before landing in Cuba.

In 2013, Cuba handed over a Florida couple, Joshua and Sharyn Hakken, who were wanted on charges that they had kidnapped their two young sons from maternal grandparents who had custody. The Hakkens fled with the children by sailboat to Havana,” said an article on philly.com.

The only caveat is Cuba treats individuals who seek political asylum quite differently than those who are fleeing for other crimes. In the past, the Cuban government would not extradite anyone who they believed sought asylum for their political beliefs.

After more than 50 years of animosity the two countries have just begun mending relations. It may take some time for Cuba and the U.S. to come to an extradition agreement.